Transcript December 21, 2012 possesses a “cryptic” numerical property

December 21, 2012 possesses
“cryptic” prime properties
Aziz S. Inan, Ph.D.
Professor, Electrical Engineering
University of Portland, Portland, Oregon
December 21, 2012
1
Last day of Long Count Mayan
Calendar-December 21, 2012
• There is general consensus that the 13baktun* Long Count Mayan Calendar cycle will
end on December 21, 2012
• Unlike all the hoax stories however, I don’t
believe that the world will come to an end on
December 21, 2012 (or any other day in 2012)
*A baktun is a period of 144,000 days (about 393 years)
in the Long Count, so, 13 baktuns is 1,872,000 days
December 21, 2012
2
December 21, 2012 has special
“cryptic” numerical properties
• In addition to being the last day of the Long
Count Mayan Calendar cycle, December 21,
2012 is also unique because its date number
possesses special “cryptic” numerical properties
• The goal of this presentation is to reveal these
cryptic numerical properties to help change the
image of this day from being a “dark,
mysterious” day to a “fun, brainteasers” day
December 21, 2012
3
December
st
21
in a leap year
• December 21st is the 356th day of each 366day leap year such as 2012
• Therefore, these two numbers (356 and 366)
together can be viewed as representing
December 21st in each leap year
• Interestingly enough, numbers 356 and 366
together are also cryptically connected to
December 21st, 2012, how?
December 21, 2012
4
December
st
21
in a leap year
• First, reverse number 356 to obtain 653
• Then, take numbers 366 and 653 and
put them side by side as 366653
• Note that number 366653 still
cryptically represents December 21st in a
leap year
• Surprisingly, this year’s December 21st
can be cryptically derived from number
366653 in two different ways
December 21, 2012
5
The 366653rd prime number
cryptically leads to 21-12-2012!
• First, the 366653rd prime number happens
to be 5280503
• Also, note that each leap year is divisible by
four
• Amazingly, four times 5280503 equals
21122012, the single full date of December
21, 2012 expressed in the day-month-year
date format! Wow!
December 21, 2012
6
Prime 356663 also cryptically
yields 21-12-2012!
•
•
•
•
•
•
Next, reverse of number 366653 is 356663
Number 356663 is the 30500th prime number
In addition, 30500 = 305 x 100
Note that four times reverse of 305 yields 2012!
Number 2012 plus 100 gives 2112!
Finally, numbers 2112 and 2012 put side by side
lead to 21122012! Fascinating!
December 21, 2012
7
Numbers 356 and 663 also
cryptically produce 21122012!
• This cryptic connection is a bit of a stretch but it is
also fun
• Remember the two numbers 356 and 366,
representing December 21st in a leap year?
• The difference of 356 and the reverse of 366 is 307
• Interestingly enough, 307 can be viewed as 305 + 2
• Twice the product of the reverses of 305 and 2
equals 2012!
December 21, 2012
8
Numbers 356 and 663 also
cryptically produce 21122012!
• Next, numbers 305 and 2 side by side make
3052
• The prime factors of 3052 are 2, 7, and 109
• Interestingly enough, 2012 + 109 – 2 – 7 =
2112!
• Again, 2112 and 2012 put side by side is
21122012! Isn’t this something?
December 21, 2012
9
December 21st in 2112 will be
very special
• As an aside, 100 years later, December 21st
in palindrome year 2112 will be a very
special calendar date, why?
• The single full date of December 21st, 2112
will be 21122112, an eight-digit palindrome
date to occur in a palindrome year!
• The last such date occurred on February 20,
2002, expressed as 20022002 and no other
such date is to occur in this millennium
December 21, 2012
10
References
1. A. S. Inan, “Numerical Oddities of December
21, 2012—Ending Date of the Long Mayan
Calendar,” December 21, 2011
https://faculty.up.edu/ainan/MayanLongCountE
nds21December2012.pdf
2. Big Primes: Large list of prime numbers
http://www.bigprimes.net/
December 21, 2012
11